Beyond Single-Shot Fidelity: Chernoff-Based Throughput Optimization in Superconducting Qubit Readout

Abstract

Single-shot fidelity is the standard benchmark for superconducting qubit readout, but it does not directly minimize the total wall-clock time required to certify a quantum state. We develop an information-theoretic description of dispersive readout by treating the measurement record as a stochastic communication channel. Within a trajectory model that incorporates T1 relaxation with full cavity memory, we compute the classical Chernoff information governing the multi-shot error exponent. We find a consistent separation between the integration time that maximizes single-shot fidelity and the time that minimizes total certification time. For representative transmon parameters and hardware overheads, the throughput-optimal integration window is longer than the fidelity-optimal one, yielding certification speedups of approximately 9 to 11 percent, with the gain saturating near 1.13x in the high-readout-power and high-overhead regime. Comparing the extracted classical information to the unit-efficiency Gaussian Chernoff benchmark defines an information-extraction efficiency metric. Typical dispersive schemes are limited to about 45 percent capture at short integration times by detection efficiency, decreasing to approximately 12 percent at a throughput-optimal integration time of about 1.22 microseconds due to T1-induced trajectory smearing. This formulation connects readout calibration to the operational objective of minimizing certification time in high-throughput superconducting processors.

Figures (5)

• Figure 1: Dynamics of information accumulation in dispersive readout. (a) Temporal evolution of the cavity coherent state separation $\Delta\alpha(t)$ following the onset of the drive pulse. The separation approaches the steady-state limit of $4\chi/\kappa$ as the resonator field rings up. (b) Integrated signal-to-noise ratio squared ($SNR^2$) as a function of integration time $\tau$. The initial quadratic growth reflects the cavity ring-up phase, transitioning to a linear regime as the steady-state signal power is reached. (c) Score distributions $p_g(x)$ and $p_e(x)$ at $\tau = 1.0~\mu$s. While the ground state is nearly Gaussian, the excited state distribution exhibits a tail extending toward the ground-state mean, a direct consequence of $T_1$ relaxation events occurring during the measurement window.
• Figure 2: Characterizing T$_1$-induced asymmetry and extraction efficiency. (a) Comparison of the excited-state score distribution $p_e(x)$ in the ideal limit (no decay) and the realistic regime ($T_1 = 30~\mu$s). The relaxation events "pollute" the score manifold, significantly shifting the optimal decision threshold. (b) The optimal Chernoff parameter $s^*$ as a function of integration time. At short $\tau$, the distributions remain nearly symmetric ($s^* \approx 0.5$), but as decay events accumulate, $s^*$ shifts toward zero, indicating that the optimal classifier becomes more biased against the excited state. (c) Information extraction efficiency $\eta_{\text{info}}$ relative to the unit-efficiency Gaussian Chernoff benchmark. The efficiency reaches its theoretical maximum of 45% (limited by detection efficiency $\eta$) at short integration times and diminishes monotonically as $\tau$ increases, reflecting the progressive information loss driven by stochastic T$_1$ relaxation during the measurement window.
• Figure 3: Systematic separation between fidelity and certification-time optima. The Bayes fidelity (primary axis) and total wall-clock certification time (secondary axis) are plotted against integration time $\tau$ for a target error $\epsilon = 10^{-4}$. Vertical dashed lines (with corresponding markers) indicate the fidelity-optimal point ($\tau_{\text{fid}}$) and the certification-optimal point ($\tau_{\text{rate}}$). The minimum in certification time occurs at a noticeably longer integration window, demonstrating that throughput optimization involves a fundamental trade-off between single-shot confidence and per-shot hardware overhead.
• Figure 4: Scaling of certification speedup across parameter space. (a) Speedup factor as a function of qubit relaxation time $T_1$ and detection efficiency $\eta$. Higher efficiencies allow the measurement to reach the certification threshold more rapidly, making the fixed hardware overhead the dominant bottleneck. The white circle marks the baseline parameters ($T_1 = 30~\mu$s, $\eta = 0.45$) used throughout this work. (b) Speedup factor as a function of steady-state photon number $\bar{n}$ and per-shot hardware overhead. The gold star indicates the maximum speedup of approximately $1.13\times$ achieved at $\bar{n}=120$ and $30~\mu$s overhead, representing the performance ceiling in the high-power, high-overhead regime.
• Figure 5: Framework validation and the Gaussian limit. (a) Calculated Chernoff information $C$ (points) compared to the analytical $SNR^2/8$ limit (line) in the absence of qubit decay ($T_1 \to \infty$). The lower panel shows residuals ($C_{\mathrm{num}} - C_{\mathrm{theory}}$), confirming excellent agreement and numerical stability. (b) Speedup factor versus per-shot overhead in the $T_1 \to \infty$ limit. The overhead axis begins at $5~\mu\text{s}$, since zero overhead is unphysical in realistic control stacks. Over this range the speedup increases monotonically with overhead, consistent with the amortization argument of Sec. II.D: the throughput optimum $\tau_{\mathrm{rate}}$ shifts to longer integration times while the fidelity optimum $\tau_{\mathrm{fid}}$ is overhead-independent.